Answer:
9
Step-by-step explanation:
Solving the equation on the left we get
(x-9)^2
Answer:
(5,3) and (10,6)
Step-by-step explanation:
The given equation y = 3x^2+9x is in the form y = ax^2+bx+c
Since a = 3 and b = 9, this means,
h = -b/(2a)
h = -9/(2*3)
h = -9/6
h = -3/2
h = -1.5
is the x coordinate of the vertex (h,k)
As a fraction, the answer is -3/2
In decimal form, that answer is -1.5
(use long division or a calculator to find that -3/2 = -1.5)
Answer:
Slopes of parallel lines are equal
Step-by-step explanation:
On a coordinate plane, quadrilateral ABCD is shown. Point A is at (-2, -2), point B is at (-3, 4), point C is at (2, 2), and point D is at (3, -4).
The slope of the line segment BC is:
![\dfrac{4-2}{-3-2} =-\dfrac{2}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B4-2%7D%7B-3-2%7D%20%3D-%5Cdfrac%7B2%7D%7B5%7D)
The slope of the line segment AD is:
![\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B-4-%28-2%29%7D%7B3-%28-2%29%7D%20%3D%5Cdfrac%7B-4%2B2%7D%7B3%2B2%7D%3D-%5Cdfrac%7B2%7D%7B5%7D)
The slope of the line segment CD is:
![\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6](https://tex.z-dn.net/?f=%5Cdfrac%7B2-%28-4%29%7D%7B2-3%7D%20%3D%5Cdfrac%7B2%2B4%7D%7B2-3%7D%3D%5Cdfrac%7B6%7D%7B-1%7D%3D-6)
The slope of the line segment BA is:
![\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6](https://tex.z-dn.net/?f=%5Cdfrac%7B4-%28-2%29%7D%7B-3-%28-2%29%7D%20%3D%5Cdfrac%7B4%2B2%7D%7B-3%2B2%7D%3D%5Cdfrac%7B6%7D%7B-1%7D%3D-6)
Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
Answer:
![5 \frac{1}{8}](https://tex.z-dn.net/?f=5%20%5Cfrac%7B1%7D%7B8%7D)
Step-by-step explanation:
Remember that
, so we want to find
. However, this is not in it's simplest form because
should be
. Therefore, the final answer is
.